Yes I agree and reading my post I can see the reason for your reply, but strength does play a part (that's what Madpensioner was saying) as Power = Strength x Speed.
Strength does play a part, there is no way to get around that, however, the degree to which it plays a part and thus the degree to which you ought to worry about/focus on it is the quandary. Ultimately, unless you are particularly puny (as in you are unable to walk up stairs or get out of a chair) or for other reasons such as physical imbalance or whatever, then you should be able to get all the necessary "strength" training required on the bike by simply riding your bike at various intensities. Given than most people have limited time to train, then it is more efficient to train on the bike. Especially since weight training often influences how well you can perform bike sessions in the following days.
At the end of the day, riding a bike, even riding a bike fast, is a series of many hundreds/thousands of hugely sub-maximal repetitions, even in short efforts. Take for example, a 3 minute Hill Climb, in 'The Rake' Hill Climb (very steep) i.e. a race (in which I was so farked, I had to be removed from my bike at the end), I averaged 75rpm for ~3.25 minutes, that is a single set of ~244 reps. On the 'Peaslows' HC, I did ~246 reps. In the National HC Champ's (a longer climb than the other two), ~808 reps. You can see, even from these basic numbers how absolutely sub-maximal each rep is. For reference (and incase anyone wants to work out the torque values), the average power for the above races was 496W, 492W & 398W respectively. I use 175mm cranks. Racing weight was 76kg.
This is not to say that strength or weight training has no benefit to general health etc, because, clearly it does! Especially for those partaking in none weight baring sports and those cracking on a bit.
